Bound-state spectra of field theories through separation of external and internal dynamics

TL;DR

This paper introduces a new method using the functional renormalisation group to compute bound state spectra by separating external and internal dynamics, exemplified in a chiral Nambu--Jona-Lasinio model.

Contribution

It develops a general strategy to calculate bound state spectra by defining dynamical coordinates as coupling parameters within the FRG framework.

Findings

Bound state spectra can be computed via scale-dependent coupling parameters.

An interaction potential among constituents is extracted in the infrared.

Quantized bound states are obtained by solving a Schrödinger eigenvalue problem.

Abstract

A general strategy is formulated for computing bound state spectra in the framework of functional renormalisation group (FRG). Dynamical "coordinates" characterising bound states are introduced as coupling parameters in the $n$-point functions of effective fields representing the bound states in an extended effective action functional. Their scale dependence is computed with functional renormalisation group equations. In the infrared an interaction potential among the constituting fields is extracted as smooth function of the coupling parameters. Eventually quantised bound state solutions are found by solving the Schr\"odinger eigenvalue problem formulated for the coupling parameters transmuted into coordinates. The proposed strategy is exemplified through the analysis of a recently published FRG study of the one-flavor chiral Nambu--Jona-Lasinio model.